Which waves require a medium through which to travel?

Mechanical waves are the correct answer because they are defined as waves that require a medium (such as air, water, or solid materials) to propagate. This includes waves like sound waves and water waves, where the oscillation of particles in the medium transmits the wave energy.

In contrast, electromagnetic waves, such as light, can travel through a vacuum and do not require a medium. Transverse and longitudinal waves are classifications that describe the direction of the particle movement relative to the direction of the wave propagation, rather than indicating whether a medium is required. For instance, both transverse and longitudinal waves can exist as mechanical waves, but electromagnetic waves do not fit into the mechanical category as they travel without a medium.